The following cards are shuffled and one is dealt to you. Then, you would toss a

Question

The following cards are shuffled and one is dealt to you. Then, you would toss an 8-sided die. The payout: If you get an ace (A) on the deal and a 5 on the toss, you get $40. If you get the 7 of clubs on the deal and an even number on the toss, you get $25. If you get any club numbered greater than or equal to 6 and an odd number on the toss, you get $30. You cost: How much should you pay in order for this game to be fair? (Assume you do not get your original money returned to you in the off chance that you win)

Explanation / Answer

Sample space = {(x,y) x: any dice orclubs and y = 1 to 8}

(x,y) (A,5) (7C, Even) (>=6C, odd number) Others Total (20*8)

Freq 1 4 20 135 160   

Prob 1/160 4/160 20./160 135/160 1

Gain 40 25 30 0

Prob*Gain 1/4 5/8 30/8 0 37/8

Expected gain = 37/8

Hence for a fair game amt to be paid = 37/8 = 4.625

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